Answer

B

Explanation

In this question, we are dealing with a circle and a tangent line. The tangent line to a circle is perpendicular to the radius at the point of tangency. This means that the angle between the radius and the tangent line is 90 degrees. Given that line segment XY is a radius and line segment YZ is a tangent, we know that the angle between XY and YZ is 90 degrees. We are also given that the length of the line segment from point X to the point on the circle is 8 units and the length of the line segment from the point on the circle to point Z is 9 units. Since the line segment from X to the point on the circle is a radius of the circle, and the line segment from the point on the circle to Z is a line segment that passes through the circle, we can use the Pythagorean theorem to find the length of ZY. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse is ZY, and the other two sides are the radius (8 units) and the line segment from the point on the circle to Z (9 units). So, we can set up the equation: ZY^2 = 8^2 + 9^2 Solving this equation gives us ZY = 15 units. Therefore, the length of ZY must be 15 units for ZY to be tangent to circle X at point Y.